Spliced messages constitute one-fourth of expressed mRNAs in the yeast Saccharomyces cerevisiae, and most mRNAs in metazoans. Splicing requires 5 ′ splice site (5 ′ SS), branch point (BP), and 3 ′ splice site (3 ′ SS) elements, but the role of the BP in splicing control is poorly understood because BP identification remains difficult. We developed a high-throughput method, Branch-seq, to map BPs and 5′ SSs of isolated RNA lariats. Applied to S. cerevisiae, Branch-seq detected 76% of expressed, annotated BPs and identified a comparable number of novel BPs. We performed RNA-seq to confirm associated 3 ′ SS locations, identifying some 200 novel splice junctions, including an AT-AC intron. We show that several yeast introns use two or even three different BPs, with effects on 3 ′ SS choice, protein coding potential, or RNA stability, and identify novel introns whose splicing changes during meiosis or in response to stress. Together, these findings show unanticipated complexity of splicing in yeast.